If you suggested Nebraska was independent, nobody would flip out, because it's nonsense. Unfortunately large industrial empires need space and resources and so it's necessary to expand beyond what might be the "real" border of your country. But who's to complain? Everyone likes the Dali Lama, but capitalism doesn't allow you to choose karma over cash.
Western China is a combination of agriculture, and completely barren, unused land. They have plenty, without Tibet and Taiwan. There's another reason, here.
The traditional explanation, AFAIK, is that China seeks a buffer around the 'Han core' (maybe the SE 2/3 of China). That buffer is Manchuria in the north, Xinjiang in the NW, Tibet in the SW, and now they seek control of the South China Sea in the south and the various seas and islands to the east. If you look at the last imperial dynasty, the Qing (~1644-1911), you can see the same map and geographical strategy. (The Communists follow the imperial dynasties in other ways too, including now a head of state for life. Will his kids follow him?)
That also follows traditional, pre-democratic great power strategy of creating a buffer region. For example, Russia is trying to do it now with Ukraine, Belarus, and Georgia (and with eyes on the Baltics), and did it in the past with the USSR and the Warsaw Pact states. Contrast that with democratic nations such as the US and those in the EU, and their relations with their neighbors.
